OpenRaiser/Intern-Atlas huggingface dataset:
Kernel Principal Component Analysis and its Applications in Face Recognition and Active Shape Models
Venue: arXiv cs.CV 2014
Year: 2014

Principal component analysis (PCA) is a popular tool for linear dimensionality reduction and feature extraction. Kernel PCA is the nonlinear form of PCA, which better exploits the complicated spatial structure of high-dimensional features. In this paper, we first review the basic ideas of PCA and kernel PCA. Then we focus on the reconstruction of pre-images for kernel PCA. We also give an introduction on how PCA is used in active shape models (ASMs), and discuss how kernel PCA can be applied to improve traditional ASMs. Then we show some experimental results to compare the performance of kernel PCA and standard PCA for classification problems. We also implement the kernel PCA-based ASMs, and use it to construct human face models.
Spectrum Coordination in Energy Efficient Cognitive Radio Networks
Venue: arXiv cs.GT 2014
Year: 2014

Device coordination in open spectrum systems is a challenging problem, particularly since users experience varying spectrum availability over time and location. In this paper, we propose a game theoretical approach that allows cognitive radio pairs, namely the primary user (PU) and the secondary user (SU), to update their transmission powers and frequencies simultaneously. Specifically, we address a Stackelberg game model in which individual users attempt to hierarchically access to the wireless spectrum while maximizing their energy efficiency. A thorough analysis of the existence, uniqueness and characterization of the Stackelberg equilibrium is conducted. In particular, we show that a spectrum coordination naturally occurs when both actors in the system decide sequentially about their powers and their transmitting carriers. As a result, spectrum sensing in such a situation turns out to be a simple detection of the presence/absence of a transmission on each sub-band. We also show that when users experience very different channel gains on their two carriers, they may choose to transmit on the same carrier at the Stackelberg equilibrium as this contributes enough energy efficiency to outweigh the interference degradation caused by the mutual transmission. Then, we provide an algorithmic analysis on how the PU and the SU can reach such a spectrum coordination using an appropriate learning process. We validate our results through extensive simulations and compare the proposed algorithm to some typical scenarios including the non-cooperative case and the throughput-based-utility systems. Typically, it is shown that the proposed Stackelberg decision approach optimizes the energy efficiency while still maximizing the throughput at the equilibrium.
The complexity of approximating conservative counting CSPs
Venue: arXiv cs.CC 2014
Year: 2014

We study the complexity of approximately solving the weighted counting constraint satisfaction problem #CSP(F). In the conservative case, where F contains all unary functions, there is a classification known for the case in which the domain of functions in F is Boolean. In this paper, we give a classification for the more general problem where functions in F have an arbitrary finite domain. We define the notions of weak log-modularity and weak log-supermodularity. We show that if F is weakly log-modular, then #CSP(F)is in FP. Otherwise, it is at least as difficult to approximate as #BIS, the problem of counting independent sets in bipartite graphs. #BIS is complete with respect to approximation-preserving reductions for a logically-defined complexity class #RHPi1, and is believed to be intractable. We further sub-divide the #BIS-hard case. If F is weakly log-supermodular, then we show that #CSP(F) is as easy as a (Boolean) log-supermodular weighted #CSP. Otherwise, we show that it is NP-hard to approximate. Finally, we give a full trichotomy for the arity-2 case, where #CSP(F) is in FP, or is #BIS-equivalent, or is equivalent in difficulty to #SAT, the problem of approximately counting the satisfying assignments of a Boolean formula in conjunctive normal form. We also discuss the algorithmic aspects of our classification.
A superlocal version of Reed's Conjecture
Venue: arXiv cs.DM 2014
Year: 2014

Reed's well-known $ω$, $Δ$, $χ$ conjecture proposes that every graph satisfies $χ\leq \lceil \frac 12(Δ+1+ω)\rceil$. The second author formulated a {\em local strengthening} of this conjecture that considers a bound supplied by the neighbourhood of a single vertex. Following the idea that the chromatic number cannot be greatly affected by any particular stable set of vertices, we propose a further strengthening that considers a bound supplied by the neighbourhoods of two adjacent vertices. We provide some fundamental evidence in support, namely that the stronger bound holds in the fractional relaxation and holds for both quasi-line graphs and graphs with stability number two. We also conjecture that in the fractional version, we can push the locality even further.
Wave-Like Solutions of General One-Dimensional Spatially Coupled Systems
Venue: arXiv cs.IT 2014
Year: 2014

We establish the existence of wave-like solutions to spatially coupled graphical models which, in the large size limit, can be characterized by a one-dimensional real-valued state. This is extended to a proof of the threshold saturation phenomenon for all such models, which includes spatially coupled irregular LDPC codes over the BEC, but also addresses hard-decision decoding for transmission over general channels, the CDMA multiple-access problem, compressed sensing, and some statistical physics models. For traditional uncoupled iterative coding systems with two components and transmission over the BEC, the asymptotic convergence behavior is completely characterized by the EXIT curves of the components. More precisely, the system converges to the desired fixed point, which is the one corresponding to perfect decoding, if and only if the two EXIT functions describing the components do not cross. For spatially coupled systems whose state is one-dimensional a closely related graphical criterion applies. Now the curves are allowed to cross, but not by too much. More precisely, we show that the threshold saturation phenomenon is related to the positivity of the (signed) area enclosed by two EXIT-like functions associated to the component systems, a very intuitive and easy-to-use graphical characterization. In the spirit of EXIT functions and Gaussian approximations, we also show how to apply the technique to higher dimensional and even infinite-dimensional cases. In these scenarios the method is no longer rigorous, but it typically gives accurate predictions. To demonstrate this application, we discuss transmission over general channels using both the belief-propagation as well as the min-sum decoder.
A Formula for the Capacity of the General Gel'fand-Pinsker Channel
Venue: arXiv cs.IT 2014
Year: 2014

We consider the Gel'fand-Pinsker problem in which the channel and state are general, i.e., possibly non-stationary, non-memoryless and non-ergodic. Using the information spectrum method and a non-trivial modification of the piggyback coding lemma by Wyner, we prove that the capacity can be expressed as an optimization over the difference of a spectral inf- and a spectral sup-mutual information rate. We consider various specializations including the case where the channel and state are memoryless but not necessarily stationary.
The Restricted Isometry Property for Random Block Diagonal Matrices
Venue: arXiv cs.IT 2014
Year: 2014

In Compressive Sensing, the Restricted Isometry Property (RIP) ensures that robust recovery of sparse vectors is possible from noisy, undersampled measurements via computationally tractable algorithms. It is by now well-known that Gaussian (or, more generally, sub-Gaussian) random matrices satisfy the RIP under certain conditions on the number of measurements. Their use can be limited in practice, however, due to storage limitations, computational considerations, or the mismatch of such matrices with certain measurement architectures. These issues have recently motivated considerable effort towards studying the RIP for structured random matrices. In this paper, we study the RIP for block diagonal measurement matrices where each block on the main diagonal is itself a sub-Gaussian random matrix. Our main result states that such matrices can indeed satisfy the RIP but that the requisite number of measurements depends on certain properties of the basis in which the signals are sparse. In the best case, these matrices perform nearly as well as dense Gaussian random matrices, despite having many fewer nonzero entries.
Modified Rice-Golomb Code for Predictive Coding of Integers with Real-valued Predictions
Venue: arXiv cs.IT 2014
Year: 2014

Rice-Golomb codes are widely used in practice to encode integer-valued prediction residuals. However, in lossless coding of audio, image, and video, specially those involving linear predictors, the predictions are from the real domain. In this paper, we have modified and extended the Rice-Golomb code so that it can operate at fractional precision to efficiently exploit the real-valued predictions. Coding at arbitrarily small precision allows the residuals to be modeled with the Laplace distribution instead of its discrete counterpart, namely the two-sided geometric distribution (TSGD). Unlike the Rice-Golomb code, which maps equally probable opposite-signed residuals to different integers, the proposed coding scheme is symmetric in the sense that, at arbitrarily small precision, it assigns codewords of equal length to equally probable residual intervals. The symmetry of both the Laplace distribution and the code facilitates the analysis of the proposed coding scheme to determine the average code-length and the optimal value of the associated coding parameter. Experimental results demonstrate that the proposed scheme, by making efficient use of real-valued predictions, achieves better compression as compared to the conventional scheme.
Metastability of Asymptotically Well-Behaved Potential Games
Venue: arXiv cs.GT 2014
Year: 2014

One of the main criticisms to game theory concerns the assumption of full rationality. Logit dynamics is a decentralized algorithm in which a level of irrationality (a.k.a. "noise") is introduced in players' behavior. In this context, the solution concept of interest becomes the logit equilibrium, as opposed to Nash equilibria. Logit equilibria are distributions over strategy profiles that possess several nice properties, including existence and uniqueness. However, there are games in which their computation may take time exponential in the number of players. We therefore look at an approximate version of logit equilibria, called metastable distributions, introduced by Auletta et al. [SODA 2012]. These are distributions that remain stable (i.e., players do not go too far from it) for a super-polynomial number of steps (rather than forever, as for logit equilibria). The hope is that these distributions exist and can be reached quickly by logit dynamics. We identify a class of potential games, called asymptotically well-behaved, for which the behavior of the logit dynamics is not chaotic as the number of players increases so to guarantee meaningful asymptotic results. We prove that any such game admits distributions which are metastable no matter the level of noise present in the system, and the starting profile of the dynamics. These distributions can be quickly reached if the rationality level is not too big when compared to the inverse of the maximum difference in potential. Our proofs build on results which may be of independent interest, including some spectral characterizations of the transition matrix defined by logit dynamics for generic games and the relationship of several convergence measures for Markov chains.
Interference in Poisson Networks with Isotropically Distributed Nodes
Venue: arXiv cs.IT 2014
Year: 2014

Practical wireless networks are finite, and hence non-stationary with nodes typically non-homo-geneously deployed over the area. This leads to a location-dependent performance and to boundary effects which are both often neglected in network modeling. In this work, interference in networks with nodes distributed according to an isotropic but not necessarily stationary Poisson point process (PPP) are studied. The resulting link performance is precisely characterized as a function of (i) an arbitrary receiver location and of (ii) an arbitrary isotropic shape of the spatial distribution. Closed-form expressions for the first moment and the Laplace transform of the interference are derived for the path loss exponents $α=2$ and $α=4$, and simple bounds are derived for other cases. The developed model is applied to practical problems in network analysis: for instance, the accuracy loss due to neglecting border effects is shown to be undesirably high within transition regions of certain deployment scenarios. Using a throughput metric not relying on the stationarity of the spatial node distribution, the spatial throughput locally around a given node is characterized.
Reconfigurable Antennas, Preemptive Switching and Virtual Channel Management
Venue: arXiv cs.IT 2014
Year: 2014

This article considers the performance of wireless communication systems that utilize reconfigurable or pattern-dynamic antennas. The focus is on finite-state channels with memory and performance is assessed in terms of real-time behavior. In a wireless setting, when a slow fading channel enters a deep fade, the corresponding communication system faces the threat of successive decoding failures at the destination. Under such circumstances, rapidly getting out of deep fades becomes a priority. Recent advances in fast reconfigurable antennas provide new means to alter the statistical profile of fading channels and thereby reduce the probability of prolonged fades. Fast reconfigurable antennas are therefore poised to improve overall performance, especially for delay-sensitive traffic in slow-fading environments. This potential for enhanced performance motivates this study of the temporal behavior of point-to-point communication systems with reconfigurable antennas. Specifically, agile wireless communication schemes over erasure channels are analyzed; situations where using reconfigurable antennas yield substantial performance gains in terms of throughput and average delay are identified. Scenarios where only partial state information is available at the receiver are also examined, naturally leading to partially observable decision processes.
A Computational Model and Convergence Theorem for Rumor Dissemination in Social Networks
Venue: arXiv cs.SI 2014
Year: 2014

The spread of rumors, which are known as unverified statements of uncertain origin, may cause tremendous number of social problems. If it would be possible to identify factors affecting spreading a rumor (such as agents' desires, trust network, etc.), then this could be used to slowdown or stop its spreading. A computational model that includes rumor features and the way a rumor is spread among society's members, based on their desires, is therefore needed. Our research is centering on the relation between the homogeneity of the society and rumor convergence in it and result shows that the homogeneity of the society is a necessary condition for convergence of the spreading rumor.
Can Selfish Groups be Self-Enforcing?
Venue: arXiv cs.DM 2014
Year: 2014

Algorithmic graph theory has thoroughly analyzed how, given a network describing constraints between various nodes, groups can be formed among these so that the resulting configuration optimizes a \emph{global} metric. In contrast, for various social and economic networks, groups are formed \emph{de facto} by the choices of selfish players. A fundamental problem in this setting is the existence and convergence to a \emph{self-enforcing} configuration: assignment of players into groups such that no player has an incentive to move into another group than hers. Motivated by information sharing on social networks -- and the difficult tradeoff between its benefits and the associated privacy risk -- we study the possible emergence of such stable configurations in a general selfish group formation game. Our paper considers this general game for the first time, and it completes its analysis. We show that convergence critically depends on the level of \emph{collusions} among the players -- which allow multiple players to move simultaneously as long as \emph{all of them} benefit. Solving a previously open problem we exactly show when, depending on collusions, convergence occurs within polynomial time, non-polynomial time, and when it never occurs. We also prove that previously known bounds on convergence time are all loose: by a novel combinatorial analysis of the evolution of this game we are able to provide the first \emph{asymptotically exact} formula on its convergence. Moreover, we extend these results by providing a complete analysis when groups may \emph{overlap}, and for general utility functions representing \emph{multi-modal} interactions. Finally, we prove that collusions have a significant and \emph{positive} effect on the \emph{efficiency} of the equilibrium that is attained.
Refinement and Difference for Probabilistic Automata
Venue: arXiv cs.LO 2014
Year: 2014

This paper studies a difference operator for stochastic systems whose specifications are represented by Abstract Probabilistic Automata (APAs). In the case refinement fails between two specifications, the target of this operator is to produce a specification APA that represents all witness PAs of this failure. Our contribution is an algorithm that allows to approximate the difference of two APAs with arbitrary precision. Our technique relies on new quantitative notions of distances between APAs used to assess convergence of the approximations, as well as on an in-depth inspection of the refinement relation for APAs. The procedure is effective and not more complex to implement than refinement checking.
StaticGreedy: solving the scalability-accuracy dilemma in influence maximization
Venue: arXiv cs.SI 2014
Year: 2014

Influence maximization, defined as a problem of finding a set of seed nodes to trigger a maximized spread of influence, is crucial to viral marketing on social networks. For practical viral marketing on large scale social networks, it is required that influence maximization algorithms should have both guaranteed accuracy and high scalability. However, existing algorithms suffer a scalability-accuracy dilemma: conventional greedy algorithms guarantee the accuracy with expensive computation, while the scalable heuristic algorithms suffer from unstable accuracy. In this paper, we focus on solving this scalability-accuracy dilemma. We point out that the essential reason of the dilemma is the surprising fact that the submodularity, a key requirement of the objective function for a greedy algorithm to approximate the optimum, is not guaranteed in all conventional greedy algorithms in the literature of influence maximization. Therefore a greedy algorithm has to afford a huge number of Monte Carlo simulations to reduce the pain caused by unguaranteed submodularity. Motivated by this critical finding, we propose a static greedy algorithm, named StaticGreedy, to strictly guarantee the submodularity of influence spread function during the seed selection process. The proposed algorithm makes the computational expense dramatically reduced by two orders of magnitude without loss of accuracy. Moreover, we propose a dynamical update strategy which can speed up the StaticGreedy algorithm by 2-7 times on large scale social networks.
Re-encoding reformulation and application to Welch-Berlekamp algorithm
Venue: arXiv cs.IT 2014
Year: 2014

The main decoding algorithms for Reed-Solomon codes are based on a bivariate interpolation step, which is expensive in time complexity. Lot of interpolation methods were proposed in order to decrease the complexity of this procedure, but they stay still expensive. Then Koetter, Ma and Vardy proposed in 2010 a technique, called re-encoding, which allows to reduce the practical running time. However, this trick is only devoted for the Koetter interpolation algorithm. We propose a reformulation of the re-encoding for any interpolation methods. The assumption for this reformulation permits only to apply it to the Welch-Berlekamp algorithm.
Cellular automata between sofic tree shifts
Venue: arXiv cs.FL 2014
Year: 2014

We study the sofic tree shifts of $A^{Σ^*}$, where $Σ^*$ is a regular rooted tree of finite rank. In particular, we give their characterization in terms of unrestricted Rabin automata. We show that if $X \subset A^{Σ^*}$ is a sofic tree shift, then the configurations in $X$ whose orbit under the shift action is finite are dense in $X$, and, as a consequence of this, we deduce that every injective cellular automata $τ\colon X \to X$ is surjective. Moreover, a characterization of sofic tree shifts in terms of general Rabin automata is given. We present an algorithm for establishing whether two unrestricted Rabin automata accept the same sofic tree shift or not. This allows us to prove the decidability of the surjectivity problem for cellular automata between sofic tree shifts. We also prove the decidability of the injectivity problem for cellular automata defined on a tree shift of finite type.
Statistical Inference in Large Antenna Arrays under Unknown Noise Pattern
Venue: arXiv cs.IT 2014
Year: 2014

In this article, a general information-plus-noise transmission model is assumed, the receiver end of which is composed of a large number of sensors and is unaware of the noise pattern. For this model, and under reasonable assumptions, a set of results is provided for the receiver to perform statistical eigen-inference on the information part. In particular, we introduce new methods for the detection, counting, and the power and subspace estimation of multiple sources composing the information part of the transmission. The theoretical performance of some of these techniques is also discussed. An exemplary application of these methods to array processing is then studied in greater detail, leading in particular to a novel MUSIC-like algorithm assuming unknown noise covariance.
Weighted $\ell_1$-minimization for generalized non-uniform sparse model
Venue: arXiv cs.IT 2014
Year: 2014

Model-based compressed sensing refers to compressed sensing with extra structure about the underlying sparse signal known a priori. Recent work has demonstrated that both for deterministic and probabilistic models imposed on the signal, this extra information can be successfully exploited to enhance recovery performance. In particular, weighted $\ell_1$-minimization with suitable choice of weights has been shown to improve performance in the so called non-uniform sparse model of signals. In this paper, we consider a full generalization of the non-uniform sparse model with very mild assumptions. We prove that when the measurements are obtained using a matrix with i.i.d Gaussian entries, weighted $\ell_1$-minimization successfully recovers the sparse signal from its measurements with overwhelming probability. We also provide a method to choose these weights for any general signal model from the non-uniform sparse class of signal models.